Hadamard matrices and links to information theory

Francisco, Carla; Oliveira, Amilcar; Grilo, Luis; Oliveira, Teresa A.

http://hdl.handle.net/10400.2/14665

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The existence of Hadamard matrices remains one of the most challenging open questions in combinatorics. Substantial progress on their existence has resulted from advances in algebraic design theory using deep connections with linear algebra, abstract algebra, finite geometry, number theory, combinatorics and optimization. The construction and analysis of Hadamard matrices, and their use on combinatorial designs, play an important role nowadays in diverse fields such as; quantum information, communications, networking, cryptography, biometry and security. Hadamard Matrices are present in our daily life and they give rise to a class of block designs named Hadamard configurations. Different applications of it based on new technologies and codes of figures such as QR Codes are present almost everywhere. BIBD are very well known as a tool to solve emerging problems in this area. Illustrations and applications to authentication codes and secret sharing schemes will be presented.